Abstract
In this article, we show that Steiner symmetrization \((n-1)\) times is sufficient to transform an ellipsoid to a ball in \({\mathbb {R}}^n\). Specifically, we seek out the \((n-1)\) directions in the unit sphere such that the destination of the corresponding Steiner symmetrization is the standard ball.
Résumé
Dans cet article, nous démontrons qu’il suffit de transformer un ellipsoïde en sphère dans \(R^n\) en utilisant \((n-1)\) fois la symétrisation de Steiner. En particulier, on trouve les \((n-1)\) directions sur la surface de la sphère unitaire de telle sorte que la destination de la symétrisation de Steiner correspondante est une sphère standard.
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21 September 2020
A Correction to this paper has been published: https://doi.org/10.1007/s40316-020-00146-2
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Acknowledgements
We are grateful to the referee for the thoughtful and careful reading given to the original draft of this paper. We also thank Jiawei Xiong and Xinbao Lu for useful discussions.
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Research of the authors was supported by NSFC No. 11871373.
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Liu, Y., Sun, Q. & Xiong, G. Steiner symmetrization \((n-1)\) times is sufficient to transform an ellipsoid to a ball in \({\mathbb {R}}^n\). Ann. Math. Québec 45, 221–228 (2021). https://doi.org/10.1007/s40316-020-00140-8
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DOI: https://doi.org/10.1007/s40316-020-00140-8